ee301 electronic circuit chapter 5 - filters

EE301 ELECTRONIC CIRCUITS

CHAPTER 5 : FILTERS

5.1 INTRODUCTION

• Is a device that removes or filters unwanted signal.• Are used to block or pass a specific range of frequencies

CATEGORIES OF FILTER

PASSIVE FILTER

ACTIVE FILTER

5.1 INTRODUCTION (cont…)

PASSIVE FILTERS ACTIVE FILTERS

Do not contain an amplifying device.

Contain some type of amplifying device.

Use resistors, capacitors and / or inductors.

Use a transistor and / or operational amplifier in combination with resistors and capacitors to obtain the desired filtering effect.

Always has insertion loss Have very low insertion loss

DIFFERENCE BETWEEN PASSIVE FILTER & ACTIVE FILTER

WHAT IS INSERTION LOSS?

• Passive filters never have a power output equal to or greater than the input because the filter always has insertion loss.

• This loss represents the difference between the power received at the load before insertion (installation) of a filter and the power after insertion.

• Is stated as the log of a ratio of power output to power input and is the result of power loss because of resistance in the circuit.

5.1 INTRODUCTION (cont…)

• Use only passive components such as inductors, capacitors and resistors.

• To minimize distortion in the filter characteristic, it is desirable to use inductors with high quality factors.

• However these are difficult to implement at frequencies below 1 kHz.

• Disadvantages:– They are particularly non-ideal (lossy)– They are bulky and expensive

5.2 PASSIVE FILTERS

5.2 PASSIVE FILTERS (cont…)

TYPES

Low-pass filter

Band-pass filter Band-stop filter

High-pass filter

Four types of filters - “Ideal”Four types of filters - “Ideal”

lowpasslowpass highpasshighpass

bandpassbandpass bandstopbandstop

5.2 PASSIVE FILTERS (cont…)

Realistic Filters:Realistic Filters:

lowpasslowpass highpasshighpass

bandpassbandpass bandstopbandstop

5.2 PASSIVE FILTERS (cont…)

5.2 PASSIVE FILTERS (cont…)

INTERACTIVE LEARNING

Ideal Filters

http://www.wisc-online.com/Objects/ViewObject.aspx?ID=ACE2603

ideal filter.swf

• Is a circuit that has a constant output voltage up to a cut-off or critical frequency, fc.

• The frequencies above fc are effectively shorted to ground and are described as being in the attenuation band, or stop-band.

• The frequencies below fc are said to be in the pass-band.

• Designed using combinations of resistors, inductors and capacitors.

5.2.1 LOW-PASS FILTER

RC LOW PASS FILTER• At low frequencies, Xc is greater than R, and

most of the input signal will appear at the output.

• The cutoff frequency occurs when Xc=R

R

C

Vin Vout

5.2.1 LOW-PASS FILTER (cont…)

R

Vin VoutL

RL LOW PASS FILTER• The inductor is shorted at low frequencies, and

most of the output voltage of the circuit dropped across R.

• At high frequencies the input acts as an open, and the majority of the input signal is dropped across L.

• RL circuit passes low frequencies and blocks high frequencies

5.2.1 LOW-PASS FILTER (cont…)

RCfc

21

Response curve for low-pass filterResponse curve for low-pass filter

Cutoff frequencyCutoff frequency

L

Rfc

2

fc

0.707 -3 dB

• When output voltage is 0.707 of the input, the power output is 50% of the input power.

• This condition exists at fc (cutoff frequency)

• If Pout = ½ Pin, then a 3 dB loss of signal has occurred.Passes low frequencies

Attenuates high frequencies

5.2.1 LOW-PASS FILTER (cont…)

• Have a wide variety of applications in electronic circuits.• One common application is in smoothing the output of a pulsating DC

signal.• The action of capacitor in an RC circuit is to resist a change in voltage

across the capacitor.• If the direct current in the circuit has a ripple, the action of the RC circuit

is to suppress or absorb the variations and to delivered a filtered DC current and voltage to the load.

A block diagram of a low-pass filter and rectifier

Example 1Determine the cutoff frequency of the circuit.

Answer : 7.23 kHz

5.2.1 LOW-PASS FILTER (cont…)

Vin VoutL

10mHR33kohm

Vin VoutR

2.2kohm

C 0.01µF

Example 2For the circuit, calculate the half-power frequency.

Answer : 52.52 kHz

• Allows frequencies above the cutoff frequency to appear at the output, but blocks or shorts to ground all those frequencies below the -3dB point on the curve.

5.2.2 HIGH-PASS FILTER

RC HIGH-PASS FILTER• Capacitive reactance is large at low frequencies

and small at high frequencies.• The capacitor acts as a coupling capacitor.

5.2.2 HIGH-PASS FILTER (cont…)

RL HIGH-PASS FILTER• There is a high value of inductive reactance at

high frequencies. The high frequencies produce a large output voltage across the inductor.

• At low frequencies, XL will be small and the low frequencies will be effectively shorted to ground.

• It should be noted that RL filter are not often used in active circuits because of their size, weight and losses.

Vin VoutR

L

Vin Vout

R

C

5.2.2 HIGH-PASS FILTER (cont…)

RCfc

21

Response curve for high-pass filterResponse curve for high-pass filter

Cutoff frequencyCutoff frequency

L

Rfc

2

• The cutoff frequency on the high-pass response curve is called the low cutoff frequency.fc

0.707 -3 dB

Passes high frequenciesAttenuates low frequencies

Example 3Design an RL high-pass filter that will have a cutoff frequency of 1500 Hz.Assume R = 1 kΩ

Answer : 106.1 mH

5.2.2 HIGH-PASS FILTER (cont…)

• Allows a certain range or band of frequencies to pass through it relatively unattenuated.

• Designed to have a very sharp, defined frequency response.• Equivalent to combining a low-pass filter and a high-pass filter.• The impedance of the circuit increases as the frequencies increase

and decrease from the resonant frequency.• Only the frequencies close to resonance are passed.• All others are blocked because of high circuit impedance.

5.2.3 BAND-PASS FILTER

5.2.3 BAND-PASS FILTER (cont…)

C L

R

IO1

IO2

IO3

IO4

LCfr

21

Resonant frequencyResonant frequency

CL R

Series resonant band-pass filter

Series resonant band-pass filter

Parallel resonant band-pass filter

Parallel resonant band-pass filter

• The cutoff frequency of the high pass section becomes the lower frequency limit in the passband f1.

• The upper frequency in the passband f2, is the result of the cutoff frequency in the low pass section.

• The passband, or bandwidth, is the difference between f2 and f1.

• At resonant frequency fr, XL = XC, and the output voltage is equal to the input signal.

f1 fr f2 f

fcfc

High pass filter

Low pass filter

Bandwidth

dB

0

-20

-40

5.2.3 BAND-PASS FILTER (cont…)

Response curve for band-pass filterResponse curve for band-pass filter

• Depending on the design and purpose of the band-pass filter, the bandwidth may be very wide or very narrow.

• Some of common uses of band-pass filters are:i. Audio – to equalize sound levelsii. Communications – to select a narrow band of radio frequencies.iii. Audio – to produce speaker crossover networks.

5.2.3 BAND-PASS FILTER (cont…)

Example 4For the circuit, calculate the resonant frequency and bandwidth.

Solution

5.2.3 BAND-PASS FILTER (cont…)

C

0.1uF

L

100mH

R100ohm

HzFmHLC

fr 55.1591)1.0)(100(2

1

2

1

HzHz

Q

frBW

F

mH

C

L

RQ

16.15910

55.1591

101.0

100

100

11

For series resonant frequencies

Example 5A parallel resonant band-pass filter has a lower cutoff frequency of 6.3 kHzand an upper cutoff frequency of 8 kHz. Determine the bandwidth and resonant frequency

Solution

5.2.3 BAND-PASS FILTER (cont…)

kHzkHzkHzfffr

kHzkHzkHzffBW

cc

cc

1.7)3.6)(8(

7.13.68

21

21

• Rejects signals at frequencies within a special band and passes signals at all other frequencies.

• Also referred to as a band-reject, notch, wave-trap, band-elimination, or band-suppression filter.

• Like the band-pass filter, the band-stop filter may also be formed by combining a low-pass and high-pass filter.

5.2.4 BAND-STOP FILTER

Low-pass filter

High-pass filter

Bandstop

fc fc• The band-stop filter is designed so

that the cutoff frequency of the low-pass filter is below that of the high-pass filter

SERIES RESONANT BAND-STOP FILTER• When a series resonant LC circuit is connected in parallel with a

load resistor, the LC network provides a low impedance shunt path.• At resonance, the LC circuits acts as a short circuit and the signal

does not pass through R.• At frequencies above or below resonance, the LC circuit offer high

resistance and current flow through the load.

5.2.4 BAND-STOP FILTER (cont…)

PARALLEL RESONANT BAND-STOP FILTER• When the parallel LC network is at resonance, the

impedance is very high and virtually no current flows to the load.

• The impedance decrease above and below resonance, so all other signals are passed through the filter.

C

L

R

C

L

R

• Popular in variety of applications, particularly audio electronics.• These filters can be used in groups to provide equalization of the

entire audio spectrum.• For example, a typical one-third octave equalizer will contain 28

band-rejection filters.• Each filter section is designed to remove a specific band of

frequencies and provides up to 15 dB attenuation at its resonant frequency.

5.2.4 BAND-STOP FILTER (cont…)

Example 6For the circuit, calculate the resonant frequency. Given L = 200 mH and C = 0.01 µF.

Solution

5.2.4 BAND-STOP FILTER (cont…)

kHzFmHLC

fr 56.3)01.0)(200(2

1

2

1

C

L

R

5.3 ACTIVE FILTERS

• Use active components or devices such as transistors and op-amps, that can amplify.

• First order filter – use one resistor and one reactive component, which is either an inductor or capacitor.

• Second order filter – use two resistors and two reactive components.

5.3 ACTIVE FILTERS (cont…)

TYPES

Low-pass filter

Band-pass filter Band-stop filter

High-pass filter

• Advantages of active filters include:– reduced size and weight, and therefore parasitic– increased reliability and improved performance– simpler design than for passive filters and can realize a wider

range of functions as well as providing voltage gain– in large quantities, the cost of an IC is less than its passive

counterpart

5.3 ACTIVE FILTERS (cont…)

• Active filters also have some disadvantages:– limited bandwidth of active devices limits the highest attainable pole

frequency and therefore applications above 100 kHz (passive RLC filters can be used up to 500 MHz)

– the achievable quality factor is also limited

– require power supplies (unlike passive filters)

– increased sensitivity to variations in circuit parameters caused by environmental changes compared to passive filters

5.3 ACTIVE FILTERS (cont…)

• For many applications, particularly in voice and data communications, the economic and performance advantages of active filters far outweigh their disadvantages.

• At low frequencies, the capacitor has an extremely high capacitive reactance.

• Therefore, the circuit acts as an inverting amplifier with a voltage gain of –Rf/R1.

• At higher frequencies, the capacitive reactance of Cf decreases.

• This causes the voltage gain to decrease due to the increased amount of negative feedback.

• When Xcf = Rf, the voltage gain equals 70.7% of its midband value.

• This is the cutoff frequency fc:

5.3.1 ACTIVE LOW-PASS FILTER

Cf

Rf1

2

3R1

Vin

Vo

20 dB/decade

fc ff CRfc

21

• The voltage gain for any frequency is calculated as

where

• The voltage gain in decibels

5.3.1 ACTIVE LOW-PASS FILTER (cont…)

1R

ZAv f

22ff

fff

XcR

RXcZ

1)( log20

R

ZAv f

dB

5.3.1 ACTIVE LOW-PASS FILTER (cont…)

Example 7Refer to figure:i) Calculate the cutoff frequency, fcii) Calculate the voltage gain at (a) 0 Hz and (b) 1 MHziii) Calculate the dB voltage gain at (a) 0 Hz and (b) 1.591 kHz.

Cf

Rf1

2

3R1

Vin

Vo1 kΩ

0.01 µF

10 kΩ

Solutioni)

ii) (a) At 0 Hz, Xcf ≈ ∞ Ω. Therefore, the voltage gain is

(b) At 1 MHz,

101

10

1

k

k

R

RAv f

9.15

10

159

9.1510

)10)(9.15(2222 k

k

k

k

XcR

RXcZ

ff

fff

5.3.1 ACTIVE LOW-PASS FILTER (cont…)

kHzFkCR

fcff

591.1)01.0)(10(2

1

2

1

9.15)01.0)(1(2

1

2

1

FMHzfCXc

ff

0159.01

9.15

1

kR

RAv f

Solutioniii) (a) At 0 Hz, Xcf ≈ ∞ Ω. Therefore, Zf = Rf

(b) The frequency 1.591 kHz is the cutoff frequency, fc.

At this frequency, Zf = 0.707 Rf = 0.707 (10 kΩ) = 7.07 kΩ.

Notice that Av is down 3 dB from its pass-band value of 20 dB

dBk

k

R

RAv

fdB 20

1

10log20log20

1)(

5.3.1 ACTIVE LOW-PASS FILTER (cont…)

dBk

k

R

ZAv

fdB 17

1

07.7log20log20

1)(

• At high frequencies, Xc1 ≈ 0 Ω and the voltage gain Av, equals –Rf/R1.

• At very low frequencies, Xc1 ≈ ∞ Ω and the voltage gain Av approaches zero.

• The cutoff frequency fc, is given by:

• At fc, the voltage gain Av, is at 70.7% of its midband value.

• The voltage gain for any frequency is calculated as

where

• Voltage gain in decibels

5.3.2 ACTIVE HIGH-PASS FILTER

112

1

CRfc

C1

Rf1

2

3R1

Vin

Vo

20 dB/decade

-3 dB

fc

1Z

RAv f 2

1211 XcRZ

1)( log20

Z

RAv f

dB

5.3.2 ACTIVE HIGH-PASS FILTER (cont…)

Example 8Refer to figure, calculate the cutoff frequency, fc.

Given C1 = 0.1 µF and R1 = 1 kΩ

Solution

C1

Rf1

2

3R1

Vin

Vo

kHzFkCR

fc 591.1)1.0)(1(2

1

2

1

11

• Besides low-pass and high-pass filters, other common types are band-pass filter (rejects high and low frequencies, passing only signal around some intermediate frequency).

• The simplest band-pass filter can be made by combining the first order low pass and high pass filters that we just looked at.

5.3.3 ACTIVE BAND-PASS FILTER

5.3.3 ACTIVE BAND-PASS FILTER (cont…)

• This circuit will attenuate low frequencies (ω<<1/R2C2) and high frequencies (ω >>1/R1C1), but will pass intermediate frequencies with a gain of -R1/R2.

• However, this circuit cannot be used to make a filter with a very narrow band. To do that requires a more complex filter.

• Figure below shows a band-pass filter using two stages, the first a high-pass filter and the second a low-pass filter, the combined operation being the desired band-pass response.

5.3.3 ACTIVE BAND-PASS FILTER (cont…)

Example 9Calculate the cutoff frequencies of the band-pass filter circuit of figure in the slide before with R1=R2=10 kΩ, C1=0.1 µF, and C2=0.002 μF.

Solution

5.3.3 ACTIVE BAND-PASS FILTER (cont…)

HzFkCR

fLP 15.159)1.0)(10(2

1

2

1

11

kHzFkCR

fHP 96.7)002.0)(10(2

1

2

1

22

• In analyzing filters, the decibel (dB) unit is often used to describe the amount of attenuation offered by the filter.

• In basic terms, the decibel is a logarithmic expression that compares two power levels.

• The power gain or loss in decibels can also be computed from a voltage ratio if the measurement are made across equal resistance.

5.4 DECIBELS & FREQUENCY RESPONSE CURVE

in

outdB V

VN log20

Where Ndb = gain or loss in decibels Vin = input voltage Vout = output voltage

Example 9In figure below, calculate the attenuation, in decibels, at the following frequencies: (a) 0 Hz, (b) 1.592 kHz, (c) 15.92 kHz. Assume that Vin = 10 Vpp at all frequencies.

Solution:a) At 0 Hz, Vout=Vin=10 Vpp,

since the capacitor C appears as an open.Therefore,

5.4 DECIBELS & FREQUENCY RESPONSE CURVE (cont…)

R

C

Vin Vout

dBV

V

P

PN

pp

pp

in

outdB 01log20

10

10log20log20

Solution:b) Since 1.592 kHz is the cutoff frequency fc, Vout will be 0.707 (Vin) or

0.707 Vpp. Therefore

c) To calculate NdB at 15.92 kHz, Xc and ZT must first determined.

5.4 DECIBELS & FREQUENCY RESPONSE CURVE (cont…)

dBV

V

P

PN

pp

pp

in

outdB 3707.0log20

10

07.7log20log20

kFkHzfC

X c 1)01.0)(92.15(2

1

2

1

kkkXRZ cT 05.10110 2222

dBk

k

Z

XN

T

cdB 200995.0log20

05.10

1log20log20

5.4 DECIBELS & FREQUENCY RESPONSE CURVE (cont…)

• In Example 9, notice that NdB is 0 dB at a frequency of 0 Hz, which is in the filter’s pass-band.

• This may seem unusual, but the 0 dB value simply indicates that there is no attenuation at this frequency.

• For an ideal passive filter, NdB = 0 dB in the pass-band.

• As another point of interest, NdB is -3 dB at the cutoff frequency of 1.592 kHz.

• Since Vout = 0.707 Vin at fc for any passive filter, NdB is always -3 dB at the cutoff frequency of a passive filter

• The NdB value of loss can be determined for any filter if the values of Vin and Vout are known